X-Nico

unusual facts about convex regular 4-polytope



4 21 polytope

Coxeter called it the Witting polytope, after Alexander Witting.

5-polytope

T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900

6-simplex

The regular 6-simplex is one of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Binary tetrahedral group

The convex hull of these 24 elements in 4-dimensional space form a convex regular 4-polytope called the 24-cell.

Cantellated 6-simplexes

The truncated 6-simplex is one of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Hanner polytope

In geometry, a Hanner polytope is a convex polytope constructed recursively by Cartesian product and polar dual operations.

Hemicube

Demihypercube, an n-dimensional uniform polytope, also known as the n-hemicube

Jim Stasheff

Stasheff's research contributions include the study of associativity in loop spaces and the construction of the associahedron (also called the Stasheff polytope), ideas leading to the theory of operads; homotopy theoretic approaches to Hilbert's fifth problem on the characterization of Lie groups; and the study of Poisson algebras in mathematical physics.

Kraanerg

Ensemble Ars Nova de l'O.R.T.F., Marius Constant (cond.) (Syrmos; Polytope; Medea; Kraanerg); Choeur d'Hommes de l'O.R.T.F. (Medea); Orchestre Philharmonique de l'O.R.T.F., Charles Bruck (cond.) (Terretektorh; Nomos gamma).

Pentellated 6-simplexes

The pentellated 6-simplex is one of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Rectified 6-simplexes

These polytopes are a part of 35 uniform 6-polytopes based on the 3,3,3,3,3 Coxeter group, all shown here in A6 Coxeter plane orthographic projections.

Semiregular polyhedron

In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope).

Uniform 2 k1 polytope

In geometry, 2k1 polytope is a uniform polytope in n dimensions (n = k+4) constructed from the Coxeter group.

Uniform k 21 polytope

In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the Coxeter group, and having only regular polytope facets.


see also